The p4a4 Conjecture -Vô Conjecture 5, Series 2(VC5S2)

We present a novel conjecture concerning sums of fourth powers and primes, named the p4a4 Conjecture . The conjecture asserts that for every integer p>1, there exists a natural number a such that p^4+a^4 is prime, a is bounded by a logarithmic function of p, and parity conditions are satisfied. This paper formulates the conjecture, discusses its plausibility, and outlines initial computational approaches.a